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Given:

Population of town is 63400

In the first year 15% and second year decreases by 20%

Calculation:

According to question,

⇒ {63400 × (115/100) × (80/100)}

⇒ 58328

∴ After 2 year later population of town is 58328

 

Formula used:

[X + Y + {(XY)/100}%]

⇒ X = 15%, and Y = - 20%

Applying the net% effect formula

⇒ [(+15 - 20) - {15 × 20}/100]

⇒ - 5 - 3 

⇒ - 8

So, (100 - 8)% of 63400

⇒ 92% of 63400

⇒ 58328

∴ After 2 year later population of town is 58328

 

1^st year 15% increase(3/20) , 2^nd year 20% decrease(1/5)

   year  =           Present pop.                last pop.

1^st year =          20                                     23

2^nd yrs =            5                                      4

After 2 yrs present pop. 100  and last pop. 92 

Given to 100 unit = 63400

⇒ 1 unit = 634

⇒ last population = 634 × 92

⇒ 58328

∴ After 2 year later population of town is 58328

Shortcut Trick

Total Time taken from 9 a.m. to 2 p.m. = 5 hours.

Distance = Speed × Time

Distance = 37 × 5 = 185 km.

∴ The correct answer is 185 km.

Alternate Method

Given:

Starting time = 9 a.m.

Arrival time = 2 p.m.

Speed of Train A = 37 km/h

Formula Used:

Distance = Speed × Time

Calculations:

⇒ Time duration = 2 p.m. − 9 a.m.

⇒ Time duration = (12 − 9) + 2 = 5 hours

⇒ Distance = 37 km/h × 5 hours

⇒ Distance = 185 km

∴ The correct answer is 185 km.

Additional Information

Speed-Distance Relation

The fundamental relation is Distance = Speed × Time. If Speed is in km/h and Time is in hours, Distance will be in km.

Unit Conversion

To convert Speed from km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Average Speed

Average Speed = Total Distance ÷ Total Time. For two equal distances with speeds x and y, Average Speed = 2xy ÷ (x + y).

Given expression:

⇒ 48% of 250 + 1050 ÷ 3 – √(?) = 423

⇒ (48/100) × 250 + 1050 ÷ 3 – √(?) = 423

⇒ (48/100) × 250 + 350 – √(?) = 423

⇒ 120 + 350 – √(?) = 423

⇒ 470 – √(?) = 423

⇒ √(?) = 470 – 423

⇒ √(?) = 47

⇒ ? = 2209

Given, 139% of 459 + $5\frac{1}{2}$ of 384

Approximating terms to the closest values, we get

⇒ 140% of 460 + 11/2 × 384

⇒ (140 × 460)/100 + 11/2 × 384

⇒ 644 + 2112 = 2756 ≈ 2760

∴ Approx value of the expression is 2760

⇒ 150 + 45 × 2(36 – 16) ÷ 18 = ?

⇒ 150 + 45 × 2(20) ÷ 18

⇒ 150 + 100 = 250

To solve questions of this type, follow the laws of “Surds and indices’’ given below -

Laws of Indices:

1. a^m × aⁿ = a^{{m + n}}
2. a^m ÷ aⁿ = a^{{m - n}}
3. (a^m)ⁿ = a^mn
4. (a)^-m = 1/a^m
5. (a)^m/n = ⁿ√a^m
6. (a)⁰ = 1

By using this laws:

⇒ (216)^7/3 × 64² × 81^5/4 = 3^-7 × 6^?

⇒ (6³)^7/3 × (2⁶)² × (3⁴)^5/4 = 3^-7 × 6^?

⇒ 6⁷ × 2¹² × 3⁵ = 3^-7 × 6^?

⇒ 6⁷ × 2¹² × 3⁵ = 3^-7 × 6^?

⇒ 6⁷ × 2¹² × 3⁵ ÷ 3^-7 = 6^?

⇒ 6⁷ × 2¹² × 3¹² = 6⁷

⇒ 6⁷ × 6¹² = 6^?

⇒ ? = 19

[3132 ÷ 29 × 48] ÷ 18 = 12 × ?

⇒ (3132/29) × 48 × ( 1/18) = 12 × ?

⇒ (108 × 48)/18 = 12 × ?

⇒ 12 × ? = 6 × 48

⇒ ? = 24

∴ ? = 24.

⇒ 76% of 395 + 48% of 135 =?

⇒ ? = 76/100 × 395 + 48/100 × 135

⇒ ? = 300.2 + 64.8

⇒ ? = 365

Follow BODMAS rule to solve this question, as per the order given below,

Step-1: Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step-2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Given expression is,

⇒ 3 + {3 + (4 - 1 × 2)} × 4 = 759 ÷ ?

⇒ 3 + {3 + (4 - 2)} × 4 = 759 ÷ ?

⇒ 3 + {3 + 2} × 4 = 759 ÷ ?

⇒ 3 + 5 × 4 = 759 ÷ ?

⇒ 3 + 20 = 759 ÷ ?

⇒ 23 = 759 ÷ ?

⇒ ? = 759/23 = 33

⇒ ? = 33

Given expression is,

⇒ 12% of (75% of (25% of (8% of 4800))) = ?

$\begin{array}{l} \Rightarrow \frac{{12}}{{100}} \times \left( {\frac{{75}}{{100}} \times \left( {\frac{{25}}{{100}} \times \left( {\frac{8}{{100}} \times 4800} \right)} \right)} \right) = ;?\ \Rightarrow \frac{3}{{25}} \times \left( {\frac{3}{4} \times \left( {\frac{1}{4} \times \left( {48 \times 8} \right)} \right)} \right) = ;?\ \Rightarrow \frac{3}{{25}} \times \left( {\frac{3}{4} \times 96} \right) = ;?\ \Rightarrow \frac{3}{{25}} \times 3 \times 24 = ;? \end{array}$

⇒ ? = 216/25 = 8.64

⇒ ? = 8.64